Let's convert each binary number to its decimal form step by step:

1. Convert 32 (Binary) to Decimal:

• 32 in binary is $100000_2$.
• To convert this to decimal: $32 = 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 32$ So, $32_2 = 32_{10}$.

2. Convert 463 (Binary) to Decimal:

• 463 in binary is $111001111_2$.
• To convert this to decimal: $463 = 1 \times 2^8 + 1 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 463$ So, $111001111_2 = 463_{10}$.

3. Convert 0.0981 (Binary) to Decimal:

• $0.0981_2$ is a fractional binary number. Let's approximate this binary fraction into a decimal by calculating up to a few significant places: $0.0981_2 = 0 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 0 \times 2^{-4} \approx 0.6016_{10}$

Thus, the approximate decimal conversion for $0.0981_2 \approx 0.6016_{10}$.

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Final Decimal Results:

• $32_2 = 32_{10}$
• $463_2 = 463_{10}$
• $0.0981_2 \approx 0.6016_{10}$

Would you like more details or have any questions?

5 Related Questions:

1. How do you convert binary numbers to decimal with more precision?
2. How does the binary system work for fractional numbers?
3. What are the rules for converting decimal numbers back into binary?
4. How can binary numbers be used in computing systems?
5. How can binary floating-point numbers be represented in standard notation?

Tip: When converting binary fractions, each digit after the decimal point corresponds to a negative power of 2 (e.g., $2^{-1}, 2^{-2}$, etc.).